The tan( Command
TAN.GIF

Command Summary

Returns the tangent of a real number.

Command Syntax

tan(angle)

Menu Location

Press TAN

Calculator Compatibility

TI-83/84/+/SE

Token Size

1 byte

tan(θ) calculates the tangent of the angle θ, which is defined by $\tan \theta=\frac{\sin \theta}{\cos \theta}$

The value returned depends on whether the calculator is in Radian or Degree mode. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion from radians to degrees is angle*180/π and from degrees to radians is angle*π/180. The tan( command also works on a list of real numbers.

Since tangent is defined as the quotient of sine divided by cosine, it is undefined for any angle such that cos(θ)=0.

In radians:

tan(π/4)
    1

In degrees:

tan(45)
    1

Advanced Uses

You can bypass the mode setting by using the ° (degree) and r (radian) symbols. These next two commands will return the same values no matter if your calculator is in degrees or radians:

tan(45°)
    1
tan(π/4^^r)
    1

Error Conditions

  • ERR:DATA TYPE is thrown if you supply a matrix or a complex argument.
  • ERR:DOMAIN is thrown if you supply an angle of π/2±nπ (in radians, where n is an integer) or 90±180n (in degrees, where n is an integer)

Related Commands

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